Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ...Robert Heward, 1833 - 150 σελίδες |
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Σελίδα 22
... Constr . equal to the distance AE , or AC . But BC ist equal to AC ; wherefore BC is not equal to BE ; for if they were equal , BE INTERC . 1. Would also be ‡ equal to AC , and it is not . And because BC is not equal to BE , the point B ...
... Constr . equal to the distance AE , or AC . But BC ist equal to AC ; wherefore BC is not equal to BE ; for if they were equal , BE INTERC . 1. Would also be ‡ equal to AC , and it is not . And because BC is not equal to BE , the point B ...
Σελίδα 27
... Constr . And if two straight lines are equal , their extremities may be made to coincide . For if when one extremity of each are made to coincide , the other extremity of the one cannot be also made to coincide with the other extremity ...
... Constr . And if two straight lines are equal , their extremities may be made to coincide . For if when one extremity of each are made to coincide , the other extremity of the one cannot be also made to coincide with the other extremity ...
Σελίδα 28
... Construction in Prop . IX ) situate in the surface of some other sphere concentric with the first and within it . Therefore the concentric sphere that cuts AB in any point that is between B and A ( that is to say , which has a radius ...
... Construction in Prop . IX ) situate in the surface of some other sphere concentric with the first and within it . Therefore the concentric sphere that cuts AB in any point that is between B and A ( that is to say , which has a radius ...
Σελίδα 32
... construction of the figure . But it has been shown that they cannot coincide in any belt or self - rejoining line in addition to CD . Wherefore they cannot coincide in any point , surface , or line as assumed . But if the surfaces of ...
... construction of the figure . But it has been shown that they cannot coincide in any belt or self - rejoining line in addition to CD . Wherefore they cannot coincide in any point , surface , or line as assumed . But if the surfaces of ...
Σελίδα 33
... Constr . Because the surfaces of these two spheres pass through the point B , which is a point in the straight line joining their centres ; + INTERC.10 . the spheres touch + one another externally in the point B. And if Cor . 8. the ...
... Constr . Because the surfaces of these two spheres pass through the point B , which is a point in the straight line joining their centres ; + INTERC.10 . the spheres touch + one another externally in the point B. And if Cor . 8. the ...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. with ... Thomas Perronet Thompson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angular points aret assigned point Axiom axis base BC bisected called CEGDHF central distances change of place circle coincide throughout Constr demonstrated double equal angles equal straight lines equal to AC equal to EF equilateral triangle Euclid exterior angle extremities four right angles Geometry given straight line greater hard body inclose a space instance INTERC Intercalary Book ist equal join line AC magnitude manner meet opposite angles parallelogram parity of reasoning pass perpendicular prolonged Prop PROPOSITION proved quadrilateral radii radius rectilinear figure remain unmoved remaining angle remains at rest respectively SCHOLIUM self-rejoining line shown side BC side opposite situation sphere whose centre straight line BC tessera THEOREM.-If third side triangle ABC turned unlimited length Wherefore